Verified answer

Answer:

x = 8

Explanation:

Given :

• The ratio of the lengths of two rods is 4 : 3.
• The ratio of their coefficients of cubical expansion is 2 : 3.
• The ratio of their linear expansion when they are heated through same temperature difference is x : 9.

To find :

the value of x

Solution :

The relation between coefficient of cubical expansion and coefficient of linear expansion is given as,

γ = 3α

where

γ denotes the coefficient of cubical expansion

α denotes the coefficient of linear expansion

As given,

γ₁ : γ₂ = 2 : 3

Then, the ratio of the coefficients of linear expansion is

α₁ : α₂ = γ₁/3 : γ₂/3

= γ₁ : γ₂

= 2 : 3

The linear expansion is given by,

∆l = lα∆T

where

l denotes the initial length

α denotes the coefficient of linear expansion

∆T denotes the change in temperature

Let l₁ and l₂ be the lengths of the two rods.

l₁ : l₂ = 4 : 3

The value of x is 8

Answer:

8

Explanation: